The news that they'd kept his death secret for as long as they did, CBS News Senior National Security Analyst Juan Zarate said Friday, was "remarkable...in part because Mullah Omar has been seen not only as the leader of the Taliban, but perhaps as the leader of this broader global movement of jihadis."

Taliban leader Mullah Omar reported dead

"To have a leader of that capacity...dead for two years is quite an achievement," he said. "That said, he was quite secretive. He was protected by folks in Pakistan. And so keeping that quiet was doable, given the fact that he was largely secretive about his movements as communications for years."

"Some of the leadership wanted to see Mullah Omar's son take over. So part of this is personality," he said. "Part of this has to do with lack of faith in the leadership of Mullah Mansour -- perhaps [he's] not as capable or charismatic or as influential, obviously, as Mullah Omar. Part of this has to do with the fact that Mullah Mansour does want to negotiate, or appears to be in favor of negotiation, whereas others in the Taliban leadership do not."

The succession dispute could sow further division among different factions within the Taliban, Zarate said, and potentially give a foothold to outside groups like the Islamic State of Iraq and Syria (ISIS) that have been trying to make inroads in Taliban territory in recent months.

It's tough to gauge how the divisions among the Taliban could affect the peace talks with the new Afghan government, Zarate said.

"I think talks will continue," he said. "If Mullah Mansour is able to ensconce his role as leader of the group, he will bring people to the table. Whether or not that means there can be a sustainable deal, and whether or not [other elements] of the Taliban network...follow along is a bigger question."